Lesson 6 | Multi-Digit and Fraction Computation | 6th Grade Mathematics

Objective

Solve problems involving division with fractions.

Common Core Standards

Core Standards

The core standards covered in this lesson

6.NS.A.1 — Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

The Number System

6.NS.A.1 — Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

Foundational Standards

The foundational standards covered in this lesson

5.NF.B.6

Number and Operations—Fractions

5.NF.B.6 — Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
5.NF.B.7

Number and Operations—Fractions

5.NF.B.7 — Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Solve fraction division problems using a variety of strategies including visual models and computation.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

The Problem Set Guidance includes many great resources for problems. The focus of this lesson is on students internalizing the concepts from the previous lessons and beginning to develop fluency with solving fraction division problems. Ensure students have ample time to solve a variety of problems and to engage in conversation with each other around solutions. It may be valuable to include any unused problems from previous lessons to reinforce the conceptual understanding. Any problems not used from the Problem Set Guidance in this lesson can be used for review at the end of the unit prior to the post-unit assessment.

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Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

Problem 1

It requires $${\frac {1}{4}}$$ of a credit to play a video game for one minute.

a. Emma has $${{\frac {7}{8}}}$$ credits. Can she play for more or less than one minute? Explain how you know.

b. How long can Emma play the video game with her $${{\frac {7}{8}}}$$ credits? How many different ways can you show the solution?

Guiding Questions

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References

Illustrative Mathematics Video Game Credits

Video Game Credits, accessed on Sept. 28, 2017, 2:04 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem 2

Solve the two problems below using a visual diagram and computation.

Problem 1:

Alisa had $${\frac {1}{2}}$$ liter of juice in a bottle. She drank $${{\frac{3}{8}}}$$ liters of juice. What fraction of the juice in the bottle did Alisa drink?

Problem 2:

Alisa had some juice in a bottle. Then she drank $${{\frac{3}{8}}}$$ liters of juice. If this was $${\frac{3}{4}}$$ of the juice that was originally in the bottle, how much juice was there to start?

Guiding Questions

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References

Illustrative Mathematics Drinking Juice, Variation 2

Drinking Juice, Variation 2, accessed on Sept. 28, 2017, 2:07 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Illustrative Mathematics Drinking Juice, Variation 3

Drinking Juice, Variation 3, accessed on Sept. 28, 2017, 2:07 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Problem Set

A set of suggested resources or problem types that teachers can turn into a problem set

Fishtank Plus Content

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

You are stuck in a big traffic jam on the freeway and you are wondering how long it will take to get to the next exit, which is $${1 \frac {1}{2}}$$ miles away. You are timing your progress and find that you travel $${\frac{2}{3}}$$ of a mile in one hour. If you continue to make progress at this rate, how long will it be until you reach the exit?

Solve the problem with a diagram and explain your answer. Then find the answer using an equation and show that it is the same as what you got in your diagram.

References

Illustrative Mathematics Traffic Jam

Traffic Jam, accessed on Sept. 14, 2017, 1:31 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Student Response

An example response to the Target Task at the level of detail expected of the students.

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Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

Illustrative Mathematics Running to School, Variation 3
Inside Mathematics Performance Assessment Tasks Grades 3-High School Rabbit Costumes
EngageNY Mathematics Grade 6 Mathematics > Module 2 > Topic A > Lesson 5 — Problem Set (Creating division stories)
EngageNY Mathematics Grade 6 Mathematics > Module 2 > Topic A > Lesson 8 — Problem Set (Dividing fractions and mixed numbers)
Illustrative Mathematics Running to School — Use the three variations to compare and contrast; note, this is a multiplication problem.
Illustrative Mathematics Running to School, Variation 2
Illustrative Mathematics Baking Cookies
EngageNY Mathematics Grade 6 Mathematics > Module 2 > Topic A > Lesson 4 — Problem Set (Interpreting and solving problems)

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Lesson 5

Lesson 7

Lesson Map

Topic A: Dividing with Fractions

Interpret division problems as the number of items in each group or the number of groups of a given number of items. Write corresponding multiplication and division problems.

6.NS.A.1

Divide a fraction by a whole number using visual models and related multiplication problems.

6.NS.A.1

Divide a whole number by a fraction using visual models.

6.NS.A.1

Use visual models and patterns to develop a general rule to divide with fractions.

6.NS.A.1

Solve and write story problems involving division with fractions.

6.NS.A.1

Solve problems involving division with fractions.

6.NS.A.1

Topic B: Computing with Decimals

Add and subtract decimals using the standard algorithm.

6.NS.B.3

Multiply decimals using strategies, and develop an understanding of the standard algorithm.

6.NS.B.3

Multiply decimals using the standard algorithm.

6.NS.B.3

Divide multi-digit whole numbers using the standard algorithm.

6.NS.B.2

Divide numbers with decimal quotients. Divide decimals by whole numbers.

6.NS.B.2 6.NS.B.3

Divide decimals by decimals using the standard algorithm.

6.NS.B.3

Solve problems involving decimals using all four operations.

6.NS.B.3

Topic C: Applying the Greatest Common Factor and the Least Common Multiple

Use prime factorization to represent numbers as products of prime factors.

6.NS.B.4

Find the greatest common factor of two numbers. Solve application problems using the greatest common factor.

6.NS.B.4

Find the least common multiple of two numbers. Solve application problems using the least common multiple.

6.NS.B.4

Solve mathematical and real-world problems using the greatest common factor and least common multiple.

6.NS.B.4

Multi-Digit and Fraction Computation

Objective

Common Core Standards

Core Standards

The Number System

Foundational Standards

Number and Operations—Fractions

Number and Operations—Fractions

Criteria for Success

Tips for Teachers

Anchor Problems

Problem 1

Guiding Questions

References

Problem 2

Guiding Questions

References

Problem Set

Target Task

References

Student Response

Additional Practice

Word Problems and Fluency Activities

Lesson Map

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